Field of the Invention
The invention relates to an apparatus for the generation of single-photon and multi-photon states using cavity-enhanced spontaneous parametric down conversion.
Brief Description of the Related Art
Spontaneous parametric down-conversion (also known as SPDC, parametric fluorescence, or parametric scattering) is a process known in quantum optics, which is used as a source of entangled photon pairs and of single photons.
The basic process involves a nonlinear crystal, that is used to split an incoming photon beam, termed a “pump beam”, into pairs of photons, called “signal” and “idler” photons. In uniform non-linear crystals, the process can happen with non-negligible efficiency only if the amplitudes of the photons in the pump beam as well as the amplitudes of the signal photons and the idler photons are in phase with each other, while the signal photons and the idler photons travel through the non-linear crystal. This condition is called “phase-matching” and corresponds to the conservation of the momentum between the pump beam, as well as the signal photons and the idler photons. According to the law of conservation of energy, the combined energies of the signal photons and the idler photons are equal to the energy of the original incoming photon in the pump beam. Therefore, the emitted photons (signal and idler photons) are correlated in frequency. The state of the non-linear crystal remains unchanged by the process of splitting the incoming photon beam.
The pairs of the signal and idler photons have correlated polarizations: if the two polarizations are identical (but orthogonal to the polarization of the pump beam) then the process is called type I. If the two polarizations are orthogonal (termed H and V for horizontal and vertical polarizations), then the process is termed type II.
Spontaneous parametric down conversion (SPDC) is used as a source of photon pairs and is triggered by random vacuum fluctuations. The photon pairs are created at random times. The conversion efficiency of SPDC is very low, on the order of 1 pair per every 1012 incoming photons. However, if one of the pair of photons (i.e. the “signal photon”) is detected at any time then its partner (the “idler photon”) is known to be present.
Efficient SPDC at the desired wavelengths can be obtained by quasi-phase-matching. The quasi phase matching technique is one that enables SPDC emission in a broad range of wavelengths. This technique comprises allowing a phase mismatch between the pump, signal and idler photons over a certain propagation distance but periodically reversing the non-linear interaction at the points where the phase mismatch would start creating destructive effects. The conservation of momentum is ensured by an additional momentum contribution corresponding to the wave vector of the periodic poling structure. This leads to a phase-matching condition which takes into account also the period of the quasi-phase-matching structure. The most used method for quasi-phase-matching is periodic poling, that is the periodic inversion of the domain orientation in a non-linear crystal, so that the sign of the non-linear coefficient also changes.
The typical frequency bandwidth of the signal photons and the idler photons emitted via SPDC is of the order of 100 GHz-1 THz. Reducing the bandwidth to MHz-level by optical filtering implies a reduction of the photon signal of 5-6 orders of magnitude.
Cavity-enhanced spontaneous parametric down conversion (CESPDC) is a more efficient method of creating narrow-bandwidth photon pairs in which the nonlinear crystal is placed within an optical resonant cavity [see Ou, Lu-PRL83, 2556-1999].
One example of the generation of a pair of entangled photons using parametric processes in a cavity is taught in U.S. Pat. No. 6,982,822 (Teich et al). A BBO (barium borate) crystal used the non-linear crystal in a non-linear configuration.
One of the main challenges in designing an apparatus for CESPDC is single-mode operation. The SPDC bandwidth is usually far larger than the free spectral range (FSR) of the cavity used. There may therefore be many resonant modes in the cavity present at the same time. One way of solving this issue is to use additional external etalons or atomic line filters to filter out the redundant resonant modes. This solution reduces the brightness, adds to bulkiness and complicates the operation of the apparatus.